The Kite Runner demonstrates the concept of belonging on many levels, in family, in friendship, in marriage, and in culture. A central inquiry throughout the book is what makes us belong to one another or to a place and culture.
Both Amir and Hassan "belong" to Baba, certainly by blood. But one of the central struggles Amir has is based on his lack of a sense of belonging to his father, and a feeling that Hassan does in fact belong.
The sense of belonging between Baba and Ali and between Amir and Hassan is complicated by the fact that Ali and Hassan are servants, and they "belong" to Baba and Amir. So, even though the relationships create an emotional sense of belonging, that feeling is overridden by the master-servant relationship, so when things turn sour, the belonging is severed.
The sense of belonging is further shown when Baba and Amir make their way to America. Interestingly, as they both struggle with belonging to a new culture, their sense of belonging to one another grows. And even while they try to be part of American culture, they both continue to feel a sense of belonging to their native culture.
The marriage of Amir and Soraya demonstrates another kind of belonging, the volutary belonging we have when we find someone to love and marry. Soraya gives Amir a sense of belonging that help Amir to fight his demons and that gives him the strength to do what he needs to do.
Sohrab is perhaps the most painful example of what it means to belong. Having been through so many traumatic experiences, as the book ends, we are left wondering if he can ever belong, to a new family, to a new land, to a new culture.